derivative of 2/(\sqrt[5]{x^2})

Lösung

\frac{d}{d x} (\frac{2}{5 x ^{2}})

- \frac{4}{5 x ^{\frac{7}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{5 x ^{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{1}{5 x ^{2}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 2 \frac{d}{d x} ((x^{2})^{- \frac{1}{5}})

Wende die Kettenregel an:

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= 2 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x)

Vereinfache

2 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x) : - \frac{4}{5 x ^{\frac{7}{5}}}

= - \frac{4}{5 x ^{\frac{7}{5}}}

\int (- 2) x d x

\int_{0}^{1} x^{2} 6 x + 8 d x

\int \frac{( 7 x ^{2} + 5 x + 7 )}{( x ^{2} + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{16}{x ^{2}} - \frac{4}{x})

d er i v a t i v e f (x) = (a^{\frac{1}{x}} + b^{\frac{1}{x}})^{x}